431 Class 24

Thomas E. Love, Ph.D.

2024-11-21

Today’s Agenda

  • Today’s example: the msleep data from the ggplot2 package in the tidyverse
  • Incorporating both single and multiple imputation to handle missing data

Today’s Packages

library(naniar)
library(janitor)
library(broom)
library(gt)
library(mosaic)      ## some nice tools for summaries
library(car)
library(GGally)
library(mice)
library(xfun) 
library(easystats)
library(tidyverse)

theme_set(theme_bw())

Mammals and How They Sleep

The mammals sleep data set (msleep)

msleep
# A tibble: 83 × 11
   name   genus vore  order conservation sleep_total sleep_rem sleep_cycle awake
   <chr>  <chr> <chr> <chr> <chr>              <dbl>     <dbl>       <dbl> <dbl>
 1 Cheet… Acin… carni Carn… lc                  12.1      NA        NA      11.9
 2 Owl m… Aotus omni  Prim… <NA>                17         1.8      NA       7  
 3 Mount… Aplo… herbi Rode… nt                  14.4       2.4      NA       9.6
 4 Great… Blar… omni  Sori… lc                  14.9       2.3       0.133   9.1
 5 Cow    Bos   herbi Arti… domesticated         4         0.7       0.667  20  
 6 Three… Brad… herbi Pilo… <NA>                14.4       2.2       0.767   9.6
 7 North… Call… carni Carn… vu                   8.7       1.4       0.383  15.3
 8 Vespe… Calo… <NA>  Rode… <NA>                 7        NA        NA      17  
 9 Dog    Canis carni Carn… domesticated        10.1       2.9       0.333  13.9
10 Roe d… Capr… herbi Arti… lc                   3        NA        NA      21  
# ℹ 73 more rows
# ℹ 2 more variables: brainwt <dbl>, bodywt <dbl>

Today’s Variables of Interest

Variable Description
name Common name of mammal
vore Carni-, insecti-, herbi- or omnivore
brainwt brain weight in kilograms
bodywt body weight in kilograms
sleep_rem REM sleep, in hours
sleep_total total amount of sleep, in hours
awake (outcome) time spent awake, in hours

Modeling Plan

Note

Note that awake = 24 - sleep_total.

We want to predict awake using four potential predictors:

  • the type of food the mammal consumes (vore)
  • the weight of the mammal’s brain (brainwt)
  • the weight of the mammal’s body, (bodywt), and
  • the proportion of total time asleep spent in REM sleep.

Creating the ms431 data

ms431 <- msleep |>
  mutate(rem_prop = sleep_rem / sleep_total) |>
  mutate(vore = factor(vore)) |>
  select(name, vore, brainwt, bodywt, rem_prop, awake)

glimpse(ms431)
Rows: 83
Columns: 6
$ name     <chr> "Cheetah", "Owl monkey", "Mountain beaver", "Greater short-ta…
$ vore     <fct> carni, omni, herbi, omni, herbi, herbi, carni, NA, carni, her…
$ brainwt  <dbl> NA, 0.01550, NA, 0.00029, 0.42300, NA, NA, NA, 0.07000, 0.098…
$ bodywt   <dbl> 50.000, 0.480, 1.350, 0.019, 600.000, 3.850, 20.490, 0.045, 1…
$ rem_prop <dbl> NA, 0.10588235, 0.16666667, 0.15436242, 0.17500000, 0.1527777…
$ awake    <dbl> 11.9, 7.0, 9.6, 9.1, 20.0, 9.6, 15.3, 17.0, 13.9, 21.0, 18.7,…

Exploring our factor variable

ms431 |> tabyl(vore) |> adorn_pct_formatting() |> gt()
vore n percent valid_percent
carni 19 22.9% 25.0%
herbi 32 38.6% 42.1%
insecti 5 6.0% 6.6%
omni 20 24.1% 26.3%
NA 7 8.4% -

Any concerns here?

Collapse to three vore groups?

favstats(awake ~ vore, data = ms431) |>
  gt() |> fmt_number(columns = min:sd, decimals = 3)
vore min Q1 median Q3 max mean sd n missing
carni 4.600 11.000 13.600 17.750 21.350 13.626 4.677 19 0
herbi 7.400 9.775 13.700 19.700 22.100 14.491 4.879 32 0
insecti 4.100 4.300 5.900 15.400 15.600 9.060 5.921 5 0
omni 6.000 13.075 14.100 14.900 16.000 13.075 2.949 20 0 
ggplot(ms431, aes(x = awake, y = vore)) + geom_boxplot()

Exploring our quantities

df_stats(~ brainwt + bodywt + rem_prop + awake, data = ms431) |>
  gt() |> fmt_number(columns = min:sd, decimals = 3)
response min Q1 median Q3 max mean sd n missing
brainwt 0.000 0.003 0.012 0.126 5.712 0.282 0.976 56 27
bodywt 0.005 0.174 1.670 41.750 6,654.000 166.136 786.840 83 0
rem_prop 0.037 0.113 0.156 0.227 0.347 0.174 0.072 61 22
awake 4.100 10.250 13.900 16.150 22.100 13.567 4.452 83 0

Any concerns here?

A brainwt of 0?

which.min(ms431$brainwt)
[1] 17
slice(ms431, 17)
# A tibble: 1 × 6
  name                      vore  brainwt bodywt rem_prop awake
  <chr>                     <fct>   <dbl>  <dbl>    <dbl> <dbl>
1 Lesser short-tailed shrew omni  0.00014  0.005    0.154  14.9
  • How many of these mammals have a brainwt below 0.01 kg?
ms431 |> filter(brainwt < 0.01) |> nrow()
[1] 23

Collinearity Check

vif(lm(awake ~ vore + bodywt + brainwt + rem_prop, data = ms431))
             GVIF Df GVIF^(1/(2*Df))
vore     1.571683  3        1.078270
bodywt   1.658313  1        1.287755
brainwt  1.459939  1        1.208280
rem_prop 1.310584  1        1.144807
cor(ms431$bodywt, ms431$brainwt, use = "complete.obs")
[1] 0.9337822
  • What can we do about this?

Change our set of variables?

What if we included

  • brain_prop: brain weight as a proportion of body weight

along with bodywt in our model?

ms431 <- ms431 |>
  mutate(brain_prop = brainwt / bodywt) |>
  select(name, vore, bodywt, brain_prop, rem_prop, awake)

vif(lm(awake ~ vore + bodywt + brain_prop + rem_prop, data = ms431))
               GVIF Df GVIF^(1/(2*Df))
vore       1.685346  3        1.090891
bodywt     1.277174  1        1.130121
brain_prop 1.330301  1        1.153387
rem_prop   1.346185  1        1.160252

OK. Let’s move on to think about missingness.

How much missingness do we have?

miss_var_summary(ms431)
# A tibble: 6 × 3
  variable   n_miss pct_miss
  <chr>       <int>    <num>
1 brain_prop     27    32.5 
2 rem_prop       22    26.5 
3 vore            7     8.43
4 name            0     0   
5 bodywt          0     0   
6 awake           0     0   
miss_case_table(ms431)
# A tibble: 4 × 3
  n_miss_in_case n_cases pct_cases
           <int>   <int>     <dbl>
1              0      43     51.8 
2              1      26     31.3 
3              2      12     14.5 
4              3       2      2.41

Missing Data Mechanisms

  • Missing completely at random There are no systematic differences between the missing values and the observed values.
    • For example, blood pressure measurements may be missing because of breakdown of an automatic sphygmomanometer.
  • Missing at random Any systematic difference between the missing and observed values can be explained by other observed data.
    • For example, missing BP measurements may be lower than measured BPs but only because younger people more often have a missing BP.
  • Missing not at random Even after the observed data are taken into account, systematic differences remain between the missing values and the observed values.
    • For example, people with high BP may be more likely to have headaches that cause them to miss clinic appointments.

“Missing at random” is an assumption that justifies the analysis, rather than a property of the data.

What assumption should we use?

Can we assume the data are MCAR, per Little’s test?

mcar_test(ms431)  ## naniar provides this function
# A tibble: 1 × 4
  statistic    df p.value missing.patterns
      <dbl> <dbl>   <dbl>            <int>
1      33.5    22  0.0549                6

With a small \(p\) value for the \(\chi^2\) test statistic, we would conclude that the ms431 data are not MCAR.

Reference

Little, Roderick J. A. 1988. “A Test of Missing Completely at Random for Multivariate Data with Missing Values.” Journal of the American Statistical Association 83 (404): 1198–1202. doi:10.1080/01621459.1988.10478722.

If not MCAR, then what?

Suppose we assume that the data are MAR. This suggests the need for imputation of missing values.

Note

If we were willing to assume MCAR, we could simply do a complete case analysis.

Here, we have complete data on our outcome (awake) and bodywt so we won’t need to impute them.

  • We will need to impute vore (7), brain_prop (27) and rem_prop (22) from our sample of 83 mammals.
  • vore is a factor, the others are quantities.

Single Imputation

We’ll create a singly imputed data set first, to select our predictors.

set.seed(12345)
ms431_imp1 <- mice(ms431, m = 1, printFlag = FALSE)
ms431_imp <- complete(ms431_imp1)

prop_complete(ms431); prop_complete(ms431_imp)
[1] 0.8875502
[1] 1

Note

After we’ve settled on a final prediction model using ms431_imp, we’ll implement multiple imputation.

Range Check for impossible values?

ms431_imp |> tabyl(vore) |> adorn_pct_formatting() |> gt()
vore n percent
carni 19 22.9%
herbi 36 43.4%
insecti 5 6.0%
omni 23 27.7% 
df_stats(~ brain_prop + bodywt + rem_prop + awake, data = ms431_imp) |>
  gt() |> fmt_number(columns = min:sd, decimals = 3)
response min Q1 median Q3 max mean sd n missing
brain_prop 0.001 0.003 0.008 0.017 0.040 0.011 0.009 83 0
bodywt 0.005 0.174 1.670 41.750 6,654.000 166.136 786.840 83 0
rem_prop 0.037 0.113 0.158 0.237 0.347 0.175 0.071 83 0
awake 4.100 10.250 13.900 16.150 22.100 13.567 4.452 83 0

Partitioning the ms431_imp data

  • Do we have a unique name to identify each mammal?
n_distinct(ms431_imp$name) == nrow(ms431_imp) # compare numbers
[1] TRUE
near(n_distinct(ms431_imp$name), nrow(ms431_imp)) # tidyverse approach
[1] TRUE
  • Partition 70% into training sample, remaining 30% to test, while maintaining a similar percentage by vore groups.
set.seed(20231128)
ms431_train <- slice_sample(ms431_imp, prop = 0.7, by = "vore")
ms431_test <- anti_join(ms431_imp, ms431_train, by = "name")

dim(ms431_train); dim(ms431_test)
[1] 57  6
[1] 26  6

Outcome transformation?

boxCox(lm(awake ~ vore + bodywt + brain_prop + rem_prop, data = ms431_train))

Scatterplot Matrix

ggpairs(ms431_train |> select(vore, bodywt, brain_prop, rem_prop, awake))

Collinearity Check in Training Sample

vif(lm(awake ~ vore + bodywt + brain_prop + rem_prop, data = ms431_train))
               GVIF Df GVIF^(1/(2*Df))
vore       1.725015  3        1.095129
bodywt     1.056919  1        1.028066
brain_prop 1.207572  1        1.098896
rem_prop   1.531482  1        1.237531

Which Potential Models Will We Fit?

  • Model 1: A simple regression on bodywt
  • Model 2: A simple regression on brain_prop
  • Model 3: A model with the two size variables (brain_prop and bodywt)
  • Model 4: Model 3 + vore
  • Model 5: Model 3 + rem_prop
  • Model 6: All four predictors

Model 6

m6 <- lm(awake ~ bodywt + brain_prop + vore + rem_prop, data = ms431_train)
model_parameters(m6, ci = 0.90) |> gt()
Parameter Coefficient SE CI CI_low CI_high t df_error p
(Intercept) 12.861509015 2.537865e+00 0.9 8.608288e+00 17.114730227 5.0678454 50 5.878093e-06
bodywt 0.001204781 5.970149e-04 0.9 2.042404e-04 0.002205321 2.0180077 50 4.897220e-02
brain_prop -83.198697107 6.012258e+01 0.9 -1.839584e+02 17.561029934 -1.3838179 50 1.725609e-01
voreherbi 1.442092605 1.601502e+00 0.9 -1.241872e+00 4.126057298 0.9004628 50 3.721908e-01
voreinsecti -7.614590737 2.500228e+00 0.9 -1.180474e+01 -3.424445527 -3.0455581 50 3.700684e-03
voreomni 0.753316104 1.637686e+00 0.9 -1.991290e+00 3.497922240 0.4599881 50 6.475188e-01
rem_prop 2.776453501 9.496943e+00 0.9 -1.313952e+01 18.692428736 0.2923523 50 7.712270e-01 
model_performance(m6) |> gt()
AIC AICc BIC R2 R2_adjusted RMSE Sigma
324.0256 327.0256 340.37 0.322219 0.2408853 3.607592 3.851854

Model 5

m5 <- lm(awake ~ bodywt + brain_prop + rem_prop, data = ms431_train)
model_parameters(m5, ci = 0.90) |> gt()
Parameter Coefficient SE CI CI_low CI_high t df_error p
(Intercept) 1.507494e+01 1.850906e+00 0.9 1.197631e+01 18.17357317 8.1446283 53 6.578536e-11
bodywt 1.359156e-03 6.426695e-04 0.9 2.832530e-04 0.00243506 2.1148606 53 3.916124e-02
brain_prop -1.022174e+02 6.214353e+01 0.9 -2.062529e+02 1.81807281 -1.6448602 53 1.059177e-01
rem_prop -6.547216e+00 8.630335e+00 0.9 -2.099540e+01 7.90096864 -0.7586282 53 4.514356e-01 
model_performance(m5) |> gt()
AIC AICc BIC R2 R2_adjusted RMSE Sigma
331.7264 332.9029 341.9417 0.1380569 0.08926767 4.068291 4.219019

Model 4

m4 <- lm(awake ~ bodywt + brain_prop + vore, data = ms431_train)
model_parameters(m4, ci = 0.90) |> gt()
Parameter Coefficient SE CI CI_low CI_high t df_error p
(Intercept) 13.524618518 1.128207e+00 0.9 1.163455e+01 15.414686173 11.9877137 51 1.875095e-16
bodywt 0.001217627 5.900331e-04 0.9 2.291540e-04 0.002206101 2.0636597 51 4.415652e-02
brain_prop -86.220983537 5.869370e+01 0.9 -1.845497e+02 12.107694999 -1.4689989 51 1.479748e-01
voreherbi 1.188933544 1.335070e+00 0.9 -1.047690e+00 3.425556767 0.8905400 51 3.773579e-01
voreinsecti -7.650136315 2.474779e+00 0.9 -1.179610e+01 -3.504177125 -3.0912408 51 3.226971e-03
voreomni 0.587367948 1.522332e+00 0.9 -1.962972e+00 3.137707806 0.3858343 51 7.012242e-01 
model_performance(m4) |> gt()
AIC AICc BIC R2 R2_adjusted RMSE Sigma
322.123 324.4087 336.4243 0.3210604 0.2544977 3.610674 3.817162

Model 3

m3 <- lm(awake ~ bodywt + brain_prop, data = ms431_train)
model_parameters(m3, ci = 0.90) |> gt()
Parameter Coefficient SE CI CI_low CI_high t df_error p
(Intercept) 13.841315609 8.805796e-01 0.9 1.236761e+01 15.315022680 15.718415 54 8.426394e-22
bodywt 0.001372401 6.399023e-04 0.9 3.014830e-04 0.002443319 2.144704 54 3.649326e-02
brain_prop -91.532194409 6.028794e+01 0.9 -1.924280e+02 9.363581154 -1.518251 54 1.347846e-01 
model_performance(m3) |> gt()
AIC AICc BIC R2 R2_adjusted RMSE Sigma
330.342 331.1113 338.5142 0.1286972 0.09642676 4.09032 4.202404

Model 2

m2 <- lm(awake ~ brain_prop, data = ms431_train)
model_parameters(m2, ci = 0.90) |> gt()
Parameter Coefficient SE CI CI_low CI_high t df_error p
(Intercept) 14.26293 0.8860011 0.9 12.78062 15.745236 16.098091 55 1.814412e-22
brain_prop -109.68223 61.6134523 0.9 -212.76363 -6.600831 -1.780167 55 8.057277e-02 
model_performance(m2) |> gt()
AIC AICc BIC R2 R2_adjusted RMSE Sigma
333.0016 333.4544 339.1307 0.0544791 0.03728781 4.260968 4.337748

Model 1

m1 <- lm(awake ~ bodywt, data = ms431_train)
model_parameters(m1, ci = 0.90) |> gt()
Parameter Coefficient SE CI CI_low CI_high t df_error p
(Intercept) 12.817198699 0.5727327039 0.9 1.18590e+01 13.775399966 22.379024 55 2.665922e-29
bodywt 0.001508777 0.0006410394 0.9 4.36296e-04 0.002581257 2.353641 55 2.219168e-02 
model_performance(m1) |> gt()
AIC AICc BIC R2 R2_adjusted RMSE Sigma
330.7247 331.1775 336.8538 0.09150414 0.07498604 4.176709 4.251971

Combining glance() results

bind_rows(glance(m1) |> mutate(name = "m1"),
          glance(m2) |> mutate(name = "m2"),
          glance(m3) |> mutate(name = "m3"),
          glance(m4) |> mutate(name = "m4"),
          glance(m5) |> mutate(name = "m5"),
          glance(m6) |> mutate(name = "m6")) |>
  select(name, r.squared, adj.r.squared, sigma, AIC, BIC, nobs, df) |>
  gt() |> fmt_number(decimals = 5, columns = 2) |>
    fmt_number(decimals = 4, columns = c(3:4)) |>
    fmt_number(decimals = 0, columns = c(5:6))
name r.squared adj.r.squared sigma AIC BIC nobs df
m1 0.09150 0.0750 4.2520 331 337 57 1
m2 0.05448 0.0373 4.3377 333 339 57 1
m3 0.12870 0.0964 4.2024 330 339 57 2
m4 0.32106 0.2545 3.8172 322 336 57 5
m5 0.13806 0.0893 4.2190 332 342 57 3
m6 0.32222 0.2409 3.8519 324 340 57 6

Compare Models

compare_performance(m1, m2, m3, m4, m5, m6, rank = TRUE)
# Comparison of Model Performance Indices

Name | Model |    R2 | R2 (adj.) |  RMSE | Sigma | AIC weights | AICc weights | BIC weights | Performance-Score
---------------------------------------------------------------------------------------------------------------
m4   |    lm | 0.321 |     0.254 | 3.611 | 3.817 |       0.700 |        0.733 |       0.382 |            99.87%
m6   |    lm | 0.322 |     0.241 | 3.608 | 3.852 |       0.270 |        0.198 |       0.053 |            65.68%
m1   |    lm | 0.092 |     0.075 | 4.177 | 4.252 |       0.009 |        0.025 |       0.308 |            20.45%
m3   |    lm | 0.129 |     0.096 | 4.090 | 4.202 |       0.011 |        0.026 |       0.134 |            20.21%
m5   |    lm | 0.138 |     0.089 | 4.068 | 4.219 |       0.006 |        0.010 |       0.024 |            15.45%
m2   |    lm | 0.054 |     0.037 | 4.261 | 4.338 |       0.003 |        0.008 |       0.099 |             2.97%

Compare Models

plot(compare_performance(m1, m2, m3, m4, m5, m6))

Check Assumptions? (m1)

check_model(m1)

Check Assumptions? (m4)

check_model(m4)

Check Assumptions? (m6)

check_model(m6)

Move forward with m1, m4 and m6

test_m1 <- augment(m1, newdata = ms431_test) |> mutate(mod = "m1")
test_m4 <- augment(m4, newdata = ms431_test) |> mutate(mod = "m4")
test_m6 <- augment(m6, newdata = ms431_test) |> mutate(mod = "m6")

test_comp <- bind_rows(test_m1, test_m4, test_m6) |>
  arrange(name, mod)

Comparing Models: Test Sample

test_comp |>
  group_by(mod) |>
  summarize(n = n(),
            MAPE = mean(abs(.resid)), 
            RMSPE = sqrt(mean(.resid^2)),
            max_error = max(abs(.resid)),
            valid_R2 = cor(awake, .fitted)^2) |>
  gt() |> fmt_number(decimals = 4, columns = -"n")
mod n MAPE RMSPE max_error valid_R2
m1 26 3.8788 4.3714 7.5530 0.1599
m4 26 4.1504 5.0685 11.1050 0.0163
m6 26 4.2407 5.1647 10.9901 0.0068

I’d probably pick model m1 or m4. But first I’ll show what happens if we pick model m6 instead, just because I want to show as much missingness as possible.

Model 6 (training sample)

m6 <- lm(awake ~ bodywt + brain_prop + vore + rem_prop, data = ms431_train)
model_parameters(m6, ci = 0.90) |> gt()
Parameter Coefficient SE CI CI_low CI_high t df_error p
(Intercept) 12.861509015 2.537865e+00 0.9 8.608288e+00 17.114730227 5.0678454 50 5.878093e-06
bodywt 0.001204781 5.970149e-04 0.9 2.042404e-04 0.002205321 2.0180077 50 4.897220e-02
brain_prop -83.198697107 6.012258e+01 0.9 -1.839584e+02 17.561029934 -1.3838179 50 1.725609e-01
voreherbi 1.442092605 1.601502e+00 0.9 -1.241872e+00 4.126057298 0.9004628 50 3.721908e-01
voreinsecti -7.614590737 2.500228e+00 0.9 -1.180474e+01 -3.424445527 -3.0455581 50 3.700684e-03
voreomni 0.753316104 1.637686e+00 0.9 -1.991290e+00 3.497922240 0.4599881 50 6.475188e-01
rem_prop 2.776453501 9.496943e+00 0.9 -1.313952e+01 18.692428736 0.2923523 50 7.712270e-01 
model_performance(m6) |> gt()
AIC AICc BIC R2 R2_adjusted RMSE Sigma
324.0256 327.0256 340.37 0.322219 0.2408853 3.607592 3.851854

Create Multiple Imputations

How many subjects have missing data that affect this model?

ms431_sub <- ms431 |> select(name, awake, bodywt, brain_prop, rem_prop, vore)

pct_miss_case(ms431_sub)
[1] 48.19277

We’ll build 50 imputed data sets.

set.seed(4312345)
ms431_mice <- mice(ms431, m = 50, printFlag = FALSE)
summary(ms431_mice)
Class: mids
Number of multiple imputations:  50 
Imputation methods:
      name       vore     bodywt brain_prop   rem_prop      awake 
        ""  "polyreg"         ""      "pmm"      "pmm"         "" 
PredictorMatrix:
           name vore bodywt brain_prop rem_prop awake
name          0    1      1          1        1     1
vore          0    0      1          1        1     1
bodywt        0    1      0          1        1     1
brain_prop    0    1      1          0        1     1
rem_prop      0    1      1          1        0     1
awake         0    1      1          1        1     0
Number of logged events:  425 
  it im      dep     meth        out
1  0  0          constant       name
2  1  1 rem_prop      pmm brain_prop
3  1  2     vore  polyreg brain_prop
4  1  2 rem_prop      pmm brain_prop
5  1  3     vore  polyreg brain_prop
6  1  3 rem_prop      pmm brain_prop

Run Model 6 on each imputation

m6_mods <- with(ms431_mice, lm(awake ~ bodywt + brain_prop + vore + rem_prop))

summary(m6_mods)
# A tibble: 350 × 6
   term          estimate std.error statistic  p.value  nobs
   <chr>            <dbl>     <dbl>     <dbl>    <dbl> <int>
 1 (Intercept)   16.2      1.80        9.00   1.35e-13    83
 2 bodywt         0.00178  0.000622    2.86   5.50e- 3    83
 3 brain_prop   -92.9     56.5        -1.64   1.04e- 1    83
 4 voreherbi     -0.104    1.26       -0.0824 9.35e- 1    83
 5 voreinsecti   -3.59     2.11       -1.70   9.32e- 2    83
 6 voreomni       0.281    1.33        0.211  8.34e- 1    83
 7 rem_prop     -10.7      7.29       -1.47   1.46e- 1    83
 8 (Intercept)   16.7      1.73        9.66   7.25e-15    83
 9 bodywt         0.00128  0.000588    2.18   3.26e- 2    83
10 brain_prop  -124.      50.6        -2.45   1.65e- 2    83
# ℹ 340 more rows

Pool Results across imputations

m6_pool <- pool(m6_mods)
model_parameters(m6_pool, ci = 0.90)
# Fixed Effects

Parameter      | Coefficient |       SE |           90% CI |     t |    df |      p
-----------------------------------------------------------------------------------
(Intercept)    |       16.55 |     2.07 | [  13.08, 20.02] |  7.99 | 49.67 | < .001
bodywt         |    1.57e-03 | 6.28e-04 | [   0.00,  0.00] |  2.51 | 67.14 | 0.015 
brain prop     |      -86.43 |    62.91 | [-191.78, 18.92] | -1.37 | 51.91 | 0.175 
vore [herbi]   |       -0.20 |     1.29 | [  -2.35,  1.95] | -0.15 | 64.44 | 0.877 
vore [insecti] |       -3.98 |     2.07 | [  -7.43, -0.54] | -1.93 | 69.69 | 0.058 
vore [omni]    |       -0.19 |     1.39 | [  -2.50,  2.12] | -0.14 | 64.60 | 0.891 
rem prop       |      -10.94 |     7.91 | [ -24.20,  2.31] | -1.38 | 48.85 | 0.173

Estimate R-square and Adjusted R-square

pool.r.squared(m6_mods)
         est      lo 95     hi 95       fmi
R^2 0.216375 0.07007382 0.3932251 0.1137024
pool.r.squared(m6_mods, adjusted = TRUE)
             est      lo 95     hi 95       fmi
adj R^2 0.154012 0.03068205 0.3286404 0.1508684

More Details on MI modeling

m6_pool
Class: mipo    m = 50 
         term  m      estimate         ubar            b            t dfcom
1 (Intercept) 50  16.547867200 3.112943e+00 1.152888e+00 4.288889e+00    76
2      bodywt 50   0.001574986 3.608544e-07 3.271760e-08 3.942264e-07    76
3  brain_prop 50 -86.427263339 2.968903e+03 9.687751e+02 3.957054e+03    76
4   voreherbi 50  -0.199673328 1.469290e+00 1.866263e-01 1.659649e+00    76
5 voreinsecti 50  -3.983083996 4.038323e+00 2.308205e-01 4.273759e+00    76
6    voreomni 50  -0.190005602 1.703208e+00 2.126782e-01 1.920140e+00    76
7    rem_prop 50 -10.940624618 4.479904e+01 1.735075e+01 6.249680e+01    76
        df        riv     lambda        fmi
1 49.66843 0.37776012 0.27418425 0.30174595
2 67.13953 0.09248037 0.08465174 0.11075252
3 51.90642 0.33283356 0.24971877 0.27704823
4 64.44489 0.12955833 0.11469822 0.14095082
5 69.69306 0.05830066 0.05508894 0.08108623
6 64.60136 0.12736657 0.11297706 0.13921982
7 48.85388 0.39504789 0.28317873 0.31082647

What if we picked model m1?

m1_mods <- with(ms431_mice, lm(awake ~ bodywt))
m1_pool <- pool(m1_mods)
model_parameters(m1_pool, ci = 0.90)
# Fixed Effects

Parameter   | Coefficient |       SE |         90% CI | t(79.06) |      p
-------------------------------------------------------------------------
(Intercept) |       13.27 |     0.48 | [12.48, 14.07] |    27.80 | < .001
bodywt      |    1.77e-03 | 5.97e-04 | [ 0.00,  0.00] |     2.96 | 0.004 
pool.r.squared(m1_mods)
           est      lo 95     hi 95          fmi
R^2 0.09733161 0.01065722 0.2444352 4.081633e-10

What if we picked model m4?

m4_mods <- with(ms431_mice, lm(awake ~ bodywt + brain_prop + vore))
m4_pool <- pool(m4_mods)
model_parameters(m4_pool, ci = 0.90)
# Fixed Effects

Parameter      | Coefficient |       SE |           90% CI |     t |    df |      p
-----------------------------------------------------------------------------------
(Intercept)    |       14.18 |     1.11 | [  12.33, 16.03] | 12.82 | 63.87 | < .001
bodywt         |    1.50e-03 | 6.04e-04 | [   0.00,  0.00] |  2.49 | 74.03 | 0.015 
brain prop     |      -76.36 |    63.63 | [-182.92, 30.20] | -1.20 | 51.74 | 0.236 
vore [herbi]   |        0.40 |     1.20 | [  -1.59,  2.40] |  0.34 | 70.78 | 0.737 
vore [insecti] |       -4.03 |     2.08 | [  -7.50, -0.56] | -1.94 | 71.22 | 0.057 
vore [omni]    |        0.08 |     1.36 | [  -2.18,  2.35] |  0.06 | 68.98 | 0.951 
pool.r.squared(m4_mods)
          est     lo 95     hi 95        fmi
R^2 0.1842649 0.0519695 0.3544588 0.06782029

Guidelines for reporting, I (Sterne)

How should we report on analyses potentially affected by missing data?

  • Report the number of missing values for each variable of interest, or the number of cases with complete data for each important component of the analysis. Give reasons for missing values if possible, and indicate how many individuals were excluded because of missing data when reporting the flow of participants through the study. If possible, describe reasons for missing data in terms of other variables (rather than just reporting a universal reason such as treatment failure.)
  • Clarify whether there are important differences between individuals with complete and incomplete data, for example, by providing a table comparing the distributions of key exposure and outcome variables in these different groups
  • Describe the type of analysis used to account for missing data (e.g., multiple imputation), and the assumptions that were made (e.g., missing at random)

Guidelines for reporting, II (Sterne)

How should we report on analyses that involve multiple imputation?

  • Provide details of the imputation modeling (software used, key settings, number of imputed datasets, variables included in imputation procedure, etc.)
  • If a large fraction of the data is imputed, compare observed and imputed values.
  • Where possible, provide results from analyses restricted to complete cases, for comparison with results based on multiple imputation. If there are important differences between the results, suggest explanations.
  • It is also desirable to investigate the robustness of key inferences to possible departures from the missing at random assumption, by assuming a range of missing not at random mechanisms in sensitivity analyses.

Session Information

xfun::session_info()
R version 4.4.2 (2024-10-31 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 11 x64 (build 22631)

Locale:
  LC_COLLATE=English_United States.utf8 
  LC_CTYPE=English_United States.utf8   
  LC_MONETARY=English_United States.utf8
  LC_NUMERIC=C                          
  LC_TIME=English_United States.utf8    

Package version:
  abind_1.4-8          askpass_1.2.1        backports_1.5.0     
  base64enc_0.1.3      bayestestR_0.15.0    bigD_0.3.0          
  bit_4.5.0            bit64_4.5.2          bitops_1.0.9        
  blob_1.2.4           boot_1.3-31          broom_1.0.7         
  bslib_0.8.0          cachem_1.1.0         callr_3.7.6         
  car_3.1-3            carData_3.0-5        cellranger_1.1.0    
  cli_3.6.3            clipr_0.8.0          coda_0.19-4.1       
  codetools_0.2-20     colorspace_2.1-1     commonmark_1.9.2    
  compiler_4.4.2       conflicted_1.2.0     correlation_0.8.6   
  cowplot_1.1.3        cpp11_0.5.0          crayon_1.5.3        
  curl_6.0.1           data.table_1.16.2    datasets_4.4.2      
  datawizard_0.13.0    DBI_1.2.3            dbplyr_2.5.0        
  Deriv_4.1.6          digest_0.6.37        doBy_4.6.24         
  dplyr_1.1.4          dtplyr_1.3.1         easystats_0.7.3     
  effectsize_0.8.9     emmeans_1.10.5       estimability_1.5.1  
  evaluate_1.0.1       fansi_1.0.6          farver_2.1.2        
  fastmap_1.2.0        fontawesome_0.5.3    forcats_1.0.0       
  foreach_1.5.2        Formula_1.2-5        fs_1.6.5            
  gargle_1.5.2         generics_0.1.3       GGally_2.2.1        
  ggformula_0.12.0     ggplot2_3.5.1        ggrepel_0.9.6       
  ggridges_0.5.6       ggstats_0.7.0        glmnet_4.1-8        
  glue_1.8.0           googledrive_2.1.1    googlesheets4_1.1.1 
  graphics_4.4.2       grDevices_4.4.2      grid_4.4.2          
  gridExtra_2.3        gt_0.11.1            gtable_0.3.6        
  haven_2.5.4          highr_0.11           hms_1.1.3           
  htmltools_0.5.8.1    htmlwidgets_1.6.4    httr_1.4.7          
  ids_1.0.1            insight_0.20.5       isoband_0.2.7       
  iterators_1.0.14     janitor_2.2.0        jomo_2.7-6          
  jquerylib_0.1.4      jsonlite_1.8.9       juicyjuice_0.1.0    
  knitr_1.49           labeling_0.4.3       labelled_2.13.0     
  lattice_0.22-6       lifecycle_1.0.4      lme4_1.1-35.5       
  lubridate_1.9.3      magrittr_2.0.3       markdown_1.13       
  MASS_7.3-61          Matrix_1.7-1         MatrixModels_0.5.3  
  memoise_2.0.1        methods_4.4.2        mgcv_1.9-1          
  mice_3.16.0          microbenchmark_1.5.0 mime_0.12           
  minqa_1.2.8          mitml_0.4-5          modelbased_0.8.9    
  modelr_0.1.11        mosaic_1.9.1         mosaicCore_0.9.4.0  
  mosaicData_0.20.4    multcomp_1.4-26      munsell_0.5.1       
  mvtnorm_1.3-2        naniar_1.1.0         nlme_3.1-166        
  nloptr_2.1.1         nnet_7.3-19          norm_1.0-11.1       
  numDeriv_2016.8.1.1  openssl_2.2.2        ordinal_2023.12.4.1 
  pan_1.9              parallel_4.4.2       parameters_0.23.0   
  patchwork_1.3.0      pbkrtest_0.5.3       performance_0.12.4  
  pillar_1.9.0         pkgconfig_2.0.3      plyr_1.8.9          
  prettyunits_1.2.0    processx_3.8.4       progress_1.2.3      
  ps_1.8.1             purrr_1.0.2          quantreg_5.99       
  R6_2.5.1             ragg_1.3.3           rappdirs_0.3.3      
  RColorBrewer_1.1-3   Rcpp_1.0.13-1        RcppEigen_0.3.4.0.2 
  reactable_0.4.4      reactR_0.6.1         readr_2.1.5         
  readxl_1.4.3         rematch_2.0.0        rematch2_2.1.2      
  report_0.5.9         reprex_2.1.1         rlang_1.1.4         
  rmarkdown_2.29       rpart_4.1.23         rstudioapi_0.17.1   
  rvest_1.0.4          sandwich_3.1-1       sass_0.4.9          
  scales_1.3.0         see_0.9.0            selectr_0.4.2       
  shape_1.4.6.1        snakecase_0.11.1     SparseM_1.84.2      
  splines_4.4.2        stats_4.4.2          stringi_1.8.4       
  stringr_1.5.1        survival_3.7-0       sys_3.4.3           
  systemfonts_1.1.0    textshaping_0.4.0    TH.data_1.1-2       
  tibble_3.2.1         tidyr_1.3.1          tidyselect_1.2.1    
  tidyverse_2.0.0      timechange_0.3.0     tinytex_0.54        
  tools_4.4.2          tzdb_0.4.0           ucminf_1.2.2        
  UpSetR_1.4.0         utf8_1.2.4           utils_4.4.2         
  uuid_1.2.1           V8_6.0.0             vctrs_0.6.5         
  viridis_0.6.5        viridisLite_0.4.2    visdat_0.6.0        
  vroom_1.6.5          withr_3.0.2          xfun_0.49           
  xml2_1.3.6           xtable_1.8-4         yaml_2.3.10         
  zoo_1.8-12

431 Class 24 | 2024-11-21 | https://thomaselove.github.io/431-2024/